Toward a Uniform Approach to the Unfolding of Nets

International audienceIn this paper we introduce the notion of spread net. Spread nets are (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and are such that vector clocks are consistent with the ticking of transitions. Such nets generalize previous families of nets like unfoldings, merged processes and trellis processes, and can thus be used to represent runs of a net in a true concurrency semantics through an operation called the spreading of a net. By contrast with previous constructions, which may identify conflicts, spread nets allow loops in time

A System of Interaction and Structure

This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulae submitted to certain equational laws typical of sequents. The calculus of structures is obtained by generalising the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allow the design of BV, yield a modular proof of cut elimination.Comment: This is the authoritative version of the article, with readable pictures, in colour, also available at . (The published version contains errors introduced by the editorial processing.) Web site for Deep Inference and the Calculus of Structures at <http://alessio.guglielmi.name/res/cos

A new operational representation of dependencies in Event Structures

The execution of an event in a complex and distributed system where the dependencies vary during the evolution of the system can be represented in many ways, and one of them is to use Context-Dependent Event structures. Event structures are related to Petri nets. The aim of this paper is to propose what can be the appropriate kind of Petri net corresponding to Context-Dependent Event structures, giving an operational flavour to the dependencies represented in a Context/Dependent Event structure. Dependencies are often operationally represented, in Petri nets, by tokens produced by activities and consumed by others. Here we shift the perspective using contextual arcs to characterize what has happened so far and in this way to describe the dependencies among the various activities

Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes

We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon. We explore basic enumeration questions in both directions: Given a polygon, how many foldings are there? Given a polytope, how many unfoldings are there to simple polygons? Throughout we give special attention to convex polygons, and to regular polygons. We show that every convex polygon folds to an infinite number of distinct polytopes, but that their number of combinatorially distinct gluings is polynomial. There are, however, simple polygons with an exponential number of distinct gluings. In the reverse direction, we show that there are polytopes with an exponential number of distinct cuttings that lead to simple unfoldings. We establish necessary conditions for a polytope to have convex unfoldings, implying, for example, that among the Platonic solids, only the tetrahedron has a convex unfolding. We provide an inventory of the polytopes that may unfold to regular polygons, showing that, for n>6, there is essentially only one class of such polytopes.Comment: 54 pages, 33 figure

Ferromagnetism in Diluted Magnetic Semiconductor Heterojunction Systems

Diluted magnetic semiconductors (DMSs), in which magnetic elements are substituted for a small fraction of host elements in a semiconductor lattice, can become ferromagnetic when doped. In this article we discuss the physics of DMS ferromagnetism in systems with semiconductor heterojunctions. We focus on the mechanism that cause magnetic and magnetoresistive properties to depend on doping profiles, defect distributions, gate voltage, and other system parameters that can in principle be engineered to yield desired results.Comment: 12 pages, 7 figures, review, special issue of Semicon. Sci. Technol. on semiconductor spintronic